Digital Material Project Multiscale Modeling of Defects in Solids: - - PowerPoint PPT Presentation

Digital Material Project

Multiscale Modeling of Defects in Solids: NSF/KDI 9873214 James P. Sethna, June 2002

Flexible Software Optimal Measures Functional Forms

People: Digital Material

Faculty, Post-Docs, Grad Students

James P. Sethna Physics Christopher R. Myers Theory Center Anthony R. Ingraffea Civil Engineering Paul R. Dawson Mechanical Engineering David Chen Taiwan University Andrew J. Dolgert Cornell Theory Center Thierry Cretegny Swiss IT company (Markus Rauscher Max Planck Institute) Nick Bailey Post-Doc with Jacobsen (Denmark) Lance Eastgate Working with Jim Langer (UCSB) Erin Iesulauro Continuing (ITR/ASP)

Veit Elser Senior personnel Nadia Adam Graduate student Erik Muller Graduate student Kevin Brown Graduate student Ankur Mathur Graduate student Daniel Freedman Graduate student Mikhail Polianski Graduate student Xi Chen Graduate student Amena Siddiqi Graduate student Siew-Ann Cheong Graduate student Catherine Morris Undergrad

Flexible Software: Digital Material

Design Patterns, Python, C++

Flexible for New Algorithms

• Nudged Elastic Band
• Acceleration Methods
• Multipoles, Interfaces
• Quasicontinuum
• FEM / MD interfaces

Python Steering (SPASM) Efficient

• Naturally Parallel
• Loop Unrolling

C++ Numerical Kernels Refactoring

• Design for Change
• Force Clean Implementation

Design Patterns

Flexible Software: Digital Material

Python Steering

from MD3D import * from Numeric import * # Sphere of atoms atoms = DynamicListOfAtoms() # Lennard Jones potential, cut off smoothly at 2.7 units potential = CutLennardJonesPotential() # Sphere of diameter = 2*radius, in box of side 5*radius # fcc has unit cell = sqrt(2) times interatomic spacing latticeConstant = potential.GetLengthScale()*sqrt(2.0) lattice = FCCLattice(latticeConstant) radius = 2.5 * latticeConstant # Put atoms in periodic boundary conditions ([0,L]x[0,L]x[0,L]) bc = SmartPeriodicBoundaryConditions() bc.SetLength(array([1, 1, 1.])*radius*5) atoms.SetBoundaryConditions(bc) # Build a spherical fcc cluster of the right spacing sphericalInitializer = SphericalClusterInitializer(radius, lattice) # Set center to center of periodic boundary conditions box # sphericalInitializer.SetCenter(array([1, 1, 1.]) * radius * 1.5) sphericalInitializer.Create(atoms)

Spherical Cluster Initializer

Flexible Software: Digital Material

Design Patterns, Python Steering, …

Molecular Dynamics, Phase-Field, Finite Elements, Quasicontinuum MD: faster than earlier Lyngby C code (learned how from Schiøtz) Flexible, Compatible: implemented quasicontinuum as MD extension Cu Interface Fracture EMT Si Notch Fracture MEAM Quasicontinuum Dislocation

Optimal Measures: Digital Material

Multipoles, Meshing to Continuum: Nick Bailey

Dislocation Peierls Barrier Nudged Elastic Band Continuum Parameters

• Barriers ⇒ Mobility
• Multipoles ⇒ Interactions

Efficient Extraction

• Transition Layer/PBC
• Multipole Continuum
• Crucial for DFT

Depinning=Saddle-Node Fast Convergence w/5-15 Multipoles

Functional Forms: Digital Material

Dislocation Mobility, 2D LJ: Nick Bailey

EB(σxx, σyy, σxy) = -(a2/2) σxy + (a2 σc/π)

×(arcsin(σxy/σc) + Σn An (1-(σxy/σc)2)n+1/2)

Symmetries: Inverting Stress EB(σxy) = EB(-σxy) – a2 σxy Singularities: Saddle-Node Transition EB(σxy) = c3/2 (σc –σxy)3/2+ c5/2 (σc –σxy)5/2… Physical Model: Sinusoidal Potential + Corrections Functional Form Taylor Series for σc, A1, A2: Nine Parameters Total Fits Entire Range (Nine Measurements / DFT Calculations!)

EB σxy σxx

σxy σxx σc

Ballistic

Functional Forms: Digital Material

Surface Energies: Thierry Cretegny

|) z

• y

| | z y | | z

• x

| | z x | | y

• x

| | y x (| 4 ) , , ( |) z | | y | | x (| 8 ) , , (

110 100

+ + + + + + + + = + + = z y x f z y x f

) ( ) (

110 100

n Bf n Af

• +

= σ

Cu: Anisotropic Surface Energy

Materials Properties anisotropic

• Surface energy depends on

surface normal (two variables)

• Grain boundary toughness

depends upon five variables

• Cusps at low-index surfaces

[T=0, grooves] Finding Good Functions: Broken Bond Model Surface energy of copper fit with two parameters (Other metals around 5)

Functional Forms: Digital Material

Functional Forms: Etching of Silicon

Markus Rauscher, Thierry Cretegny, Melissa Hines, Rik Wind Etching rate has cusps at low-index surfaces Etching rate jumps are associated with a faceting transition First-order: nucleation

CACTUS, FFTW CCMR, Microsoft